Reasons for nonlinear stress-strain curves in shear of unidirectional glass fibre composite are analysed. Laminate with stacking sequence [45/-45]s is used in tensile quasi-static as well as in tensile creep and strain recovery tests to study the development of viscoelastic and viscoplastic shear strains in local coordinates of the ply. It is shown that Zapa’s integral representation of viscoplasticity is applicable for this material and methodology for parameter determination is given. Schapery’s nonlinear viscoelastic material model was used for shear response characterization and the nonlinearity parameters’ dependence on the shear stress was determined and described by fitting functions. Microdamage development is quantified by measuring axial modulus and Poisson’s ratio of the laminate. The obtained nonlinear viscoelastic, viscoplastic model with included effect of microdamage was successfully used to predict the nonlinear shear stress-strain curve in strain controlled tensile loading.